Numeric.SpecFunctions:incompleteBetaApprox from math-functions-0.1.5.2, B

Percentage Accurate: 96.7% → 99.5%

Time: 15.0s

Alternatives: 17

Speedup: 1.0×

• 40.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x * exp(((y * (log(z) - t)) + (a * (log((1.0 - z)) - b))));
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x * exp(((y * (log(z) - t)) + (a * (log((1.0d0 - z)) - b))))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x * Math.exp(((y * (Math.log(z) - t)) + (a * (Math.log((1.0 - z)) - b))));
}

Python

def code(x, y, z, t, a, b):
	return x * math.exp(((y * (math.log(z) - t)) + (a * (math.log((1.0 - z)) - b))))

Julia

function code(x, y, z, t, a, b)
	return Float64(x * exp(Float64(Float64(y * Float64(log(z) - t)) + Float64(a * Float64(log(Float64(1.0 - z)) - b)))))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x * exp(((y * (log(z) - t)) + (a * (log((1.0 - z)) - b))));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x * N[Exp[N[(N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[Log[N[(1.0 - z), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Initial Program: 96.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x * exp(((y * (log(z) - t)) + (a * (log((1.0 - z)) - b))));
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x * exp(((y * (log(z) - t)) + (a * (log((1.0d0 - z)) - b))))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x * Math.exp(((y * (Math.log(z) - t)) + (a * (Math.log((1.0 - z)) - b))));
}

Python

def code(x, y, z, t, a, b):
	return x * math.exp(((y * (math.log(z) - t)) + (a * (math.log((1.0 - z)) - b))))

Julia

function code(x, y, z, t, a, b)
	return Float64(x * exp(Float64(Float64(y * Float64(log(z) - t)) + Float64(a * Float64(log(Float64(1.0 - z)) - b)))))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x * exp(((y * (log(z) - t)) + (a * (log((1.0 - z)) - b))));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x * N[Exp[N[(N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[Log[N[(1.0 - z), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ x \cdot e^{\mathsf{fma}\left(y, \log z - t, a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)\right)} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (* x (exp (fma y (- (log z) t) (* a (- (log1p (- z)) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x * exp(fma(y, (log(z) - t), (a * (log1p(-z) - b))));
}

Julia

function code(x, y, z, t, a, b)
	return Float64(x * exp(fma(y, Float64(log(z) - t), Float64(a * Float64(log1p(Float64(-z)) - b)))))
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x * N[Exp[N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision] + N[(a * N[(N[Log[1 + (-z)], $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.1%

   \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
2. Step-by-step derivation

   1. fma-define 96.5%

      \[\leadsto x \cdot e^{\color{blue}{\mathsf{fma}\left(y, \log z - t, a \cdot \left(\log \left(1 - z\right) - b\right)\right)}} \]

   2. sub-neg 96.5%

      \[\leadsto x \cdot e^{\mathsf{fma}\left(y, \log z - t, a \cdot \left(\log \color{blue}{\left(1 + \left(-z\right)\right)} - b\right)\right)} \]

   3. log1p-define 100.0%

      \[\leadsto x \cdot e^{\mathsf{fma}\left(y, \log z - t, a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)\right)} \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{x \cdot e^{\mathsf{fma}\left(y, \log z - t, a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)\right)}} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 96.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x * exp(((y * (log(z) - t)) + (a * (log((1.0 - z)) - b))));
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x * exp(((y * (log(z) - t)) + (a * (log((1.0d0 - z)) - b))))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x * Math.exp(((y * (Math.log(z) - t)) + (a * (Math.log((1.0 - z)) - b))));
}

Python

def code(x, y, z, t, a, b):
	return x * math.exp(((y * (math.log(z) - t)) + (a * (math.log((1.0 - z)) - b))))

Julia

function code(x, y, z, t, a, b)
	return Float64(x * exp(Float64(Float64(y * Float64(log(z) - t)) + Float64(a * Float64(log(Float64(1.0 - z)) - b)))))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x * exp(((y * (log(z) - t)) + (a * (log((1.0 - z)) - b))));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x * N[Exp[N[(N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[Log[N[(1.0 - z), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.1%

   \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 3: 85.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-48} \lor \neg \left(y \leq 1.22 \cdot 10^{-85}\right):\\ \;\;\;\;x \cdot {\left(\frac{z}{e^{t}}\right)}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-\left(z + b\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.3e-48) (not (<= y 1.22e-85)))
   (* x (pow (/ z (exp t)) y))
   (* x (exp (* a (- (+ z b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.3e-48) || !(y <= 1.22e-85)) {
		tmp = x * pow((z / exp(t)), y);
	} else {
		tmp = x * exp((a * -(z + b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-3.3d-48)) .or. (.not. (y <= 1.22d-85))) then
        tmp = x * ((z / exp(t)) ** y)
    else
        tmp = x * exp((a * -(z + b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.3e-48) || !(y <= 1.22e-85)) {
		tmp = x * Math.pow((z / Math.exp(t)), y);
	} else {
		tmp = x * Math.exp((a * -(z + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -3.3e-48) or not (y <= 1.22e-85):
		tmp = x * math.pow((z / math.exp(t)), y)
	else:
		tmp = x * math.exp((a * -(z + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3.3e-48) || !(y <= 1.22e-85))
		tmp = Float64(x * (Float64(z / exp(t)) ^ y));
	else
		tmp = Float64(x * exp(Float64(a * Float64(-Float64(z + b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -3.3e-48) || ~((y <= 1.22e-85)))
		tmp = x * ((z / exp(t)) ^ y);
	else
		tmp = x * exp((a * -(z + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3.3e-48], N[Not[LessEqual[y, 1.22e-85]], $MachinePrecision]], N[(x * N[Power[N[(z / N[Exp[t], $MachinePrecision]), $MachinePrecision], y], $MachinePrecision]), $MachinePrecision], N[(x * N[Exp[N[(a * (-N[(z + b), $MachinePrecision])), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.3e-48 or 1.22000000000000006e-85 < y

   1. Initial program 99.3%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 90.4%

      \[\leadsto x \cdot \color{blue}{e^{y \cdot \left(\log z - t\right)}} \]
   4. Step-by-step derivation

      1. *-commutative 90.4%

         \[\leadsto x \cdot e^{\color{blue}{\left(\log z - t\right) \cdot y}} \]

      2. exp-prod 90.4%

         \[\leadsto x \cdot \color{blue}{{\left(e^{\log z - t}\right)}^{y}} \]

      3. exp-diff 90.4%

         \[\leadsto x \cdot {\color{blue}{\left(\frac{e^{\log z}}{e^{t}}\right)}}^{y} \]

      4. rem-exp-log 90.4%

         \[\leadsto x \cdot {\left(\frac{\color{blue}{z}}{e^{t}}\right)}^{y} \]

   5. Simplified 90.4%

      \[\leadsto x \cdot \color{blue}{{\left(\frac{z}{e^{t}}\right)}^{y}} \]

   if -3.3e-48 < y < 1.22000000000000006e-85

   1. Initial program 91.9%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 81.0%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\log \left(1 - z\right) - b\right)}} \]
   4. Step-by-step derivation

      1. sub-neg 81.0%

         \[\leadsto x \cdot e^{a \cdot \left(\log \color{blue}{\left(1 + \left(-z\right)\right)} - b\right)} \]

      2. log1p-define 89.1%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 89.1%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in z around 0 89.1%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(a \cdot b\right) + -1 \cdot \left(a \cdot z\right)}} \]
   7. Step-by-step derivation

      1. +-commutative 89.1%

         \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(a \cdot z\right) + -1 \cdot \left(a \cdot b\right)}} \]

      2. associate-*r* 89.1%

         \[\leadsto x \cdot e^{\color{blue}{\left(-1 \cdot a\right) \cdot z} + -1 \cdot \left(a \cdot b\right)} \]

      3. associate-*r* 89.1%

         \[\leadsto x \cdot e^{\left(-1 \cdot a\right) \cdot z + \color{blue}{\left(-1 \cdot a\right) \cdot b}} \]

      4. distribute-lft-out 89.1%

         \[\leadsto x \cdot e^{\color{blue}{\left(-1 \cdot a\right) \cdot \left(z + b\right)}} \]

      5. mul-1-neg 89.1%

         \[\leadsto x \cdot e^{\color{blue}{\left(-a\right)} \cdot \left(z + b\right)} \]

   8. Simplified 89.1%

      \[\leadsto x \cdot e^{\color{blue}{\left(-a\right) \cdot \left(z + b\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-48} \lor \neg \left(y \leq 1.22 \cdot 10^{-85}\right):\\ \;\;\;\;x \cdot {\left(\frac{z}{e^{t}}\right)}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-\left(z + b\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 96.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ x \cdot e^{y \cdot \left(\log z - t\right) - a \cdot b} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (* x (exp (- (* y (- (log z) t)) (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x * exp(((y * (log(z) - t)) - (a * b)));
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x * exp(((y * (log(z) - t)) - (a * b)))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x * Math.exp(((y * (Math.log(z) - t)) - (a * b)));
}

Python

def code(x, y, z, t, a, b):
	return x * math.exp(((y * (math.log(z) - t)) - (a * b)))

Julia

function code(x, y, z, t, a, b)
	return Float64(x * exp(Float64(Float64(y * Float64(log(z) - t)) - Float64(a * b))))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x * exp(((y * (log(z) - t)) - (a * b)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x * N[Exp[N[(N[(y * N[(N[Log[z], $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.1%

   \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
2. Add Preprocessing

3. Taylor expanded in z around 0 95.0%

   \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(a \cdot b\right) + y \cdot \left(\log z - t\right)}} \]

4. Final simplification 95.0%

   \[\leadsto x \cdot e^{y \cdot \left(\log z - t\right) - a \cdot b} \]
5. Add Preprocessing

Alternative 5: 71.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot {z}^{y}\\ t_2 := x \cdot e^{y \cdot \left(-t\right)}\\ \mathbf{if}\;t \leq -2 \cdot 10^{+18}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.26 \cdot 10^{-175}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-197}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-58}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (pow z y))) (t_2 (* x (exp (* y (- t))))))
   (if (<= t -2e+18)
     t_2
     (if (<= t -2.26e-175)
       t_1
       (if (<= t 1.05e-197)
         (* x (exp (* a (- b))))
         (if (<= t 5e-58) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * pow(z, y);
	double t_2 = x * exp((y * -t));
	double tmp;
	if (t <= -2e+18) {
		tmp = t_2;
	} else if (t <= -2.26e-175) {
		tmp = t_1;
	} else if (t <= 1.05e-197) {
		tmp = x * exp((a * -b));
	} else if (t <= 5e-58) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (z ** y)
    t_2 = x * exp((y * -t))
    if (t <= (-2d+18)) then
        tmp = t_2
    else if (t <= (-2.26d-175)) then
        tmp = t_1
    else if (t <= 1.05d-197) then
        tmp = x * exp((a * -b))
    else if (t <= 5d-58) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * Math.pow(z, y);
	double t_2 = x * Math.exp((y * -t));
	double tmp;
	if (t <= -2e+18) {
		tmp = t_2;
	} else if (t <= -2.26e-175) {
		tmp = t_1;
	} else if (t <= 1.05e-197) {
		tmp = x * Math.exp((a * -b));
	} else if (t <= 5e-58) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.pow(z, y)
	t_2 = x * math.exp((y * -t))
	tmp = 0
	if t <= -2e+18:
		tmp = t_2
	elif t <= -2.26e-175:
		tmp = t_1
	elif t <= 1.05e-197:
		tmp = x * math.exp((a * -b))
	elif t <= 5e-58:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * (z ^ y))
	t_2 = Float64(x * exp(Float64(y * Float64(-t))))
	tmp = 0.0
	if (t <= -2e+18)
		tmp = t_2;
	elseif (t <= -2.26e-175)
		tmp = t_1;
	elseif (t <= 1.05e-197)
		tmp = Float64(x * exp(Float64(a * Float64(-b))));
	elseif (t <= 5e-58)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (z ^ y);
	t_2 = x * exp((y * -t));
	tmp = 0.0;
	if (t <= -2e+18)
		tmp = t_2;
	elseif (t <= -2.26e-175)
		tmp = t_1;
	elseif (t <= 1.05e-197)
		tmp = x * exp((a * -b));
	elseif (t <= 5e-58)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[Exp[N[(y * (-t)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2e+18], t$95$2, If[LessEqual[t, -2.26e-175], t$95$1, If[LessEqual[t, 1.05e-197], N[(x * N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5e-58], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2e18 or 4.99999999999999977e-58 < t

   1. Initial program 98.5%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 78.9%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 78.9%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 78.9%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 78.9%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 78.9%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   if -2e18 < t < -2.2599999999999999e-175 or 1.05e-197 < t < 4.99999999999999977e-58

   1. Initial program 92.4%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 71.2%

      \[\leadsto x \cdot \color{blue}{e^{y \cdot \left(\log z - t\right)}} \]
   4. Step-by-step derivation

      1. *-commutative 71.2%

         \[\leadsto x \cdot e^{\color{blue}{\left(\log z - t\right) \cdot y}} \]

      2. exp-prod 70.0%

         \[\leadsto x \cdot \color{blue}{{\left(e^{\log z - t}\right)}^{y}} \]

      3. exp-diff 70.0%

         \[\leadsto x \cdot {\color{blue}{\left(\frac{e^{\log z}}{e^{t}}\right)}}^{y} \]

      4. rem-exp-log 70.1%

         \[\leadsto x \cdot {\left(\frac{\color{blue}{z}}{e^{t}}\right)}^{y} \]

   5. Simplified 70.1%

      \[\leadsto x \cdot \color{blue}{{\left(\frac{z}{e^{t}}\right)}^{y}} \]

   6. Taylor expanded in t around 0 71.3%

      \[\leadsto x \cdot \color{blue}{{z}^{y}} \]

   if -2.2599999999999999e-175 < t < 1.05e-197

   1. Initial program 95.4%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 73.7%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(a \cdot b\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 73.7%

         \[\leadsto x \cdot e^{\color{blue}{-a \cdot b}} \]

      2. distribute-rgt-neg-out 73.7%

         \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

   5. Simplified 73.7%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 72.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot {z}^{y}\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{-8}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+135} \lor \neg \left(y \leq 4.05 \cdot 10^{+158}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (pow z y))))
   (if (<= y -1.65e-17)
     t_1
     (if (<= y 1.32e-8)
       (* x (exp (* a (- b))))
       (if (or (<= y 3.8e+135) (not (<= y 4.05e+158)))
         t_1
         (* (* y t) (- x)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * pow(z, y);
	double tmp;
	if (y <= -1.65e-17) {
		tmp = t_1;
	} else if (y <= 1.32e-8) {
		tmp = x * exp((a * -b));
	} else if ((y <= 3.8e+135) || !(y <= 4.05e+158)) {
		tmp = t_1;
	} else {
		tmp = (y * t) * -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (z ** y)
    if (y <= (-1.65d-17)) then
        tmp = t_1
    else if (y <= 1.32d-8) then
        tmp = x * exp((a * -b))
    else if ((y <= 3.8d+135) .or. (.not. (y <= 4.05d+158))) then
        tmp = t_1
    else
        tmp = (y * t) * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * Math.pow(z, y);
	double tmp;
	if (y <= -1.65e-17) {
		tmp = t_1;
	} else if (y <= 1.32e-8) {
		tmp = x * Math.exp((a * -b));
	} else if ((y <= 3.8e+135) || !(y <= 4.05e+158)) {
		tmp = t_1;
	} else {
		tmp = (y * t) * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.pow(z, y)
	tmp = 0
	if y <= -1.65e-17:
		tmp = t_1
	elif y <= 1.32e-8:
		tmp = x * math.exp((a * -b))
	elif (y <= 3.8e+135) or not (y <= 4.05e+158):
		tmp = t_1
	else:
		tmp = (y * t) * -x
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * (z ^ y))
	tmp = 0.0
	if (y <= -1.65e-17)
		tmp = t_1;
	elseif (y <= 1.32e-8)
		tmp = Float64(x * exp(Float64(a * Float64(-b))));
	elseif ((y <= 3.8e+135) || !(y <= 4.05e+158))
		tmp = t_1;
	else
		tmp = Float64(Float64(y * t) * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (z ^ y);
	tmp = 0.0;
	if (y <= -1.65e-17)
		tmp = t_1;
	elseif (y <= 1.32e-8)
		tmp = x * exp((a * -b));
	elseif ((y <= 3.8e+135) || ~((y <= 4.05e+158)))
		tmp = t_1;
	else
		tmp = (y * t) * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.65e-17], t$95$1, If[LessEqual[y, 1.32e-8], N[(x * N[Exp[N[(a * (-b)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 3.8e+135], N[Not[LessEqual[y, 4.05e+158]], $MachinePrecision]], t$95$1, N[(N[(y * t), $MachinePrecision] * (-x)), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.65e-17 or 1.32000000000000007e-8 < y < 3.8000000000000001e135 or 4.0499999999999999e158 < y

   1. Initial program 99.1%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 90.3%

      \[\leadsto x \cdot \color{blue}{e^{y \cdot \left(\log z - t\right)}} \]
   4. Step-by-step derivation

      1. *-commutative 90.3%

         \[\leadsto x \cdot e^{\color{blue}{\left(\log z - t\right) \cdot y}} \]

      2. exp-prod 90.3%

         \[\leadsto x \cdot \color{blue}{{\left(e^{\log z - t}\right)}^{y}} \]

      3. exp-diff 90.3%

         \[\leadsto x \cdot {\color{blue}{\left(\frac{e^{\log z}}{e^{t}}\right)}}^{y} \]

      4. rem-exp-log 90.3%

         \[\leadsto x \cdot {\left(\frac{\color{blue}{z}}{e^{t}}\right)}^{y} \]

   5. Simplified 90.3%

      \[\leadsto x \cdot \color{blue}{{\left(\frac{z}{e^{t}}\right)}^{y}} \]

   6. Taylor expanded in t around 0 67.7%

      \[\leadsto x \cdot \color{blue}{{z}^{y}} \]

   if -1.65e-17 < y < 1.32000000000000007e-8

   1. Initial program 92.9%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 77.2%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(a \cdot b\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 77.2%

         \[\leadsto x \cdot e^{\color{blue}{-a \cdot b}} \]

      2. distribute-rgt-neg-out 77.2%

         \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

   5. Simplified 77.2%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

   if 3.8000000000000001e135 < y < 4.0499999999999999e158

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 85.9%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 85.9%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 85.9%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 85.9%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 85.9%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 32.9%

      \[\leadsto \color{blue}{x + -1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 32.9%

         \[\leadsto x + \color{blue}{\left(-t \cdot \left(x \cdot y\right)\right)} \]

      2. unsub-neg 32.9%

         \[\leadsto \color{blue}{x - t \cdot \left(x \cdot y\right)} \]

      3. *-commutative 32.9%

         \[\leadsto x - \color{blue}{\left(x \cdot y\right) \cdot t} \]

      4. *-commutative 32.9%

         \[\leadsto x - \color{blue}{\left(y \cdot x\right)} \cdot t \]

      5. associate-*l* 32.9%

         \[\leadsto x - \color{blue}{y \cdot \left(x \cdot t\right)} \]

      6. *-commutative 32.9%

         \[\leadsto x - y \cdot \color{blue}{\left(t \cdot x\right)} \]

   8. Simplified 32.9%

      \[\leadsto \color{blue}{x - y \cdot \left(t \cdot x\right)} \]

   9. Taylor expanded in y around inf 32.9%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 32.9%

          \[\leadsto \color{blue}{-t \cdot \left(x \cdot y\right)} \]

       2. *-commutative 32.9%

          \[\leadsto -\color{blue}{\left(x \cdot y\right) \cdot t} \]

       3. associate-*r* 73.3%

          \[\leadsto -\color{blue}{x \cdot \left(y \cdot t\right)} \]

       4. *-commutative 73.3%

          \[\leadsto -\color{blue}{\left(y \cdot t\right) \cdot x} \]

       5. distribute-rgt-neg-in 73.3%

          \[\leadsto \color{blue}{\left(y \cdot t\right) \cdot \left(-x\right)} \]

   11. Simplified 73.3%

       \[\leadsto \color{blue}{\left(y \cdot t\right) \cdot \left(-x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-17}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{-8}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-b\right)}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+135} \lor \neg \left(y \leq 4.05 \cdot 10^{+158}\right):\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.5% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot {z}^{y}\\ \mathbf{if}\;y \leq -8.6 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-43}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-\left(z + b\right)\right)}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+109}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (pow z y))))
   (if (<= y -8.6e+19)
     t_1
     (if (<= y 3.1e-43)
       (* x (exp (* a (- (+ z b)))))
       (if (<= y 6.8e+109) t_1 (* x (exp (* y (- t)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * pow(z, y);
	double tmp;
	if (y <= -8.6e+19) {
		tmp = t_1;
	} else if (y <= 3.1e-43) {
		tmp = x * exp((a * -(z + b)));
	} else if (y <= 6.8e+109) {
		tmp = t_1;
	} else {
		tmp = x * exp((y * -t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (z ** y)
    if (y <= (-8.6d+19)) then
        tmp = t_1
    else if (y <= 3.1d-43) then
        tmp = x * exp((a * -(z + b)))
    else if (y <= 6.8d+109) then
        tmp = t_1
    else
        tmp = x * exp((y * -t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * Math.pow(z, y);
	double tmp;
	if (y <= -8.6e+19) {
		tmp = t_1;
	} else if (y <= 3.1e-43) {
		tmp = x * Math.exp((a * -(z + b)));
	} else if (y <= 6.8e+109) {
		tmp = t_1;
	} else {
		tmp = x * Math.exp((y * -t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * math.pow(z, y)
	tmp = 0
	if y <= -8.6e+19:
		tmp = t_1
	elif y <= 3.1e-43:
		tmp = x * math.exp((a * -(z + b)))
	elif y <= 6.8e+109:
		tmp = t_1
	else:
		tmp = x * math.exp((y * -t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * (z ^ y))
	tmp = 0.0
	if (y <= -8.6e+19)
		tmp = t_1;
	elseif (y <= 3.1e-43)
		tmp = Float64(x * exp(Float64(a * Float64(-Float64(z + b)))));
	elseif (y <= 6.8e+109)
		tmp = t_1;
	else
		tmp = Float64(x * exp(Float64(y * Float64(-t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (z ^ y);
	tmp = 0.0;
	if (y <= -8.6e+19)
		tmp = t_1;
	elseif (y <= 3.1e-43)
		tmp = x * exp((a * -(z + b)));
	elseif (y <= 6.8e+109)
		tmp = t_1;
	else
		tmp = x * exp((y * -t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.6e+19], t$95$1, If[LessEqual[y, 3.1e-43], N[(x * N[Exp[N[(a * (-N[(z + b), $MachinePrecision])), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.8e+109], t$95$1, N[(x * N[Exp[N[(y * (-t)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.6e19 or 3.0999999999999999e-43 < y < 6.80000000000000013e109

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 92.2%

      \[\leadsto x \cdot \color{blue}{e^{y \cdot \left(\log z - t\right)}} \]
   4. Step-by-step derivation

      1. *-commutative 92.2%

         \[\leadsto x \cdot e^{\color{blue}{\left(\log z - t\right) \cdot y}} \]

      2. exp-prod 92.2%

         \[\leadsto x \cdot \color{blue}{{\left(e^{\log z - t}\right)}^{y}} \]

      3. exp-diff 92.2%

         \[\leadsto x \cdot {\color{blue}{\left(\frac{e^{\log z}}{e^{t}}\right)}}^{y} \]

      4. rem-exp-log 92.2%

         \[\leadsto x \cdot {\left(\frac{\color{blue}{z}}{e^{t}}\right)}^{y} \]

   5. Simplified 92.2%

      \[\leadsto x \cdot \color{blue}{{\left(\frac{z}{e^{t}}\right)}^{y}} \]

   6. Taylor expanded in t around 0 67.9%

      \[\leadsto x \cdot \color{blue}{{z}^{y}} \]

   if -8.6e19 < y < 3.0999999999999999e-43

   1. Initial program 93.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 78.5%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\log \left(1 - z\right) - b\right)}} \]
   4. Step-by-step derivation

      1. sub-neg 78.5%

         \[\leadsto x \cdot e^{a \cdot \left(\log \color{blue}{\left(1 + \left(-z\right)\right)} - b\right)} \]

      2. log1p-define 86.1%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 86.1%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in z around 0 86.1%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(a \cdot b\right) + -1 \cdot \left(a \cdot z\right)}} \]
   7. Step-by-step derivation

      1. +-commutative 86.1%

         \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(a \cdot z\right) + -1 \cdot \left(a \cdot b\right)}} \]

      2. associate-*r* 86.1%

         \[\leadsto x \cdot e^{\color{blue}{\left(-1 \cdot a\right) \cdot z} + -1 \cdot \left(a \cdot b\right)} \]

      3. associate-*r* 86.1%

         \[\leadsto x \cdot e^{\left(-1 \cdot a\right) \cdot z + \color{blue}{\left(-1 \cdot a\right) \cdot b}} \]

      4. distribute-lft-out 86.1%

         \[\leadsto x \cdot e^{\color{blue}{\left(-1 \cdot a\right) \cdot \left(z + b\right)}} \]

      5. mul-1-neg 86.1%

         \[\leadsto x \cdot e^{\color{blue}{\left(-a\right)} \cdot \left(z + b\right)} \]

   8. Simplified 86.1%

      \[\leadsto x \cdot e^{\color{blue}{\left(-a\right) \cdot \left(z + b\right)}} \]

   if 6.80000000000000013e109 < y

   1. Initial program 98.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 72.2%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 72.2%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 72.2%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 72.2%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 72.2%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{+19}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-43}:\\ \;\;\;\;x \cdot e^{a \cdot \left(-\left(z + b\right)\right)}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+109}:\\ \;\;\;\;x \cdot {z}^{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot e^{y \cdot \left(-t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 54.4% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{+33}:\\ \;\;\;\;y \cdot \left(x \cdot \left(\frac{1}{y} - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot {z}^{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.15e+33) (* y (* x (- (/ 1.0 y) t))) (* x (pow z y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.15e+33) {
		tmp = y * (x * ((1.0 / y) - t));
	} else {
		tmp = x * pow(z, y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-2.15d+33)) then
        tmp = y * (x * ((1.0d0 / y) - t))
    else
        tmp = x * (z ** y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.15e+33) {
		tmp = y * (x * ((1.0 / y) - t));
	} else {
		tmp = x * Math.pow(z, y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.15e+33:
		tmp = y * (x * ((1.0 / y) - t))
	else:
		tmp = x * math.pow(z, y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.15e+33)
		tmp = Float64(y * Float64(x * Float64(Float64(1.0 / y) - t)));
	else
		tmp = Float64(x * (z ^ y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.15e+33)
		tmp = y * (x * ((1.0 / y) - t));
	else
		tmp = x * (z ^ y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.15e+33], N[(y * N[(x * N[(N[(1.0 / y), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.15000000000000014e33

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 80.5%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 80.5%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 80.5%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 80.5%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 80.5%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 24.7%

      \[\leadsto \color{blue}{x + -1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 24.7%

         \[\leadsto x + \color{blue}{\left(-t \cdot \left(x \cdot y\right)\right)} \]

      2. unsub-neg 24.7%

         \[\leadsto \color{blue}{x - t \cdot \left(x \cdot y\right)} \]

      3. *-commutative 24.7%

         \[\leadsto x - \color{blue}{\left(x \cdot y\right) \cdot t} \]

      4. *-commutative 24.7%

         \[\leadsto x - \color{blue}{\left(y \cdot x\right)} \cdot t \]

      5. associate-*l* 27.7%

         \[\leadsto x - \color{blue}{y \cdot \left(x \cdot t\right)} \]

      6. *-commutative 27.7%

         \[\leadsto x - y \cdot \color{blue}{\left(t \cdot x\right)} \]

   8. Simplified 27.7%

      \[\leadsto \color{blue}{x - y \cdot \left(t \cdot x\right)} \]

   9. Taylor expanded in y around inf 29.3%

      \[\leadsto \color{blue}{y \cdot \left(\frac{x}{y} - t \cdot x\right)} \]

   10. Taylor expanded in x around 0 31.0%

       \[\leadsto y \cdot \color{blue}{\left(x \cdot \left(\frac{1}{y} - t\right)\right)} \]

   if -2.15000000000000014e33 < t

   1. Initial program 95.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 71.0%

      \[\leadsto x \cdot \color{blue}{e^{y \cdot \left(\log z - t\right)}} \]
   4. Step-by-step derivation

      1. *-commutative 71.0%

         \[\leadsto x \cdot e^{\color{blue}{\left(\log z - t\right) \cdot y}} \]

      2. exp-prod 67.2%

         \[\leadsto x \cdot \color{blue}{{\left(e^{\log z - t}\right)}^{y}} \]

      3. exp-diff 67.2%

         \[\leadsto x \cdot {\color{blue}{\left(\frac{e^{\log z}}{e^{t}}\right)}}^{y} \]

      4. rem-exp-log 67.3%

         \[\leadsto x \cdot {\left(\frac{\color{blue}{z}}{e^{t}}\right)}^{y} \]

   5. Simplified 67.3%

      \[\leadsto x \cdot \color{blue}{{\left(\frac{z}{e^{t}}\right)}^{y}} \]

   6. Taylor expanded in t around 0 64.2%

      \[\leadsto x \cdot \color{blue}{{z}^{y}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 26.6% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+181} \lor \neg \left(y \leq 1.55 \cdot 10^{-68}\right):\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.7e+181) (not (<= y 1.55e-68)))
   (* (* y t) (- x))
   (- x (* a (* x z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.7e+181) || !(y <= 1.55e-68)) {
		tmp = (y * t) * -x;
	} else {
		tmp = x - (a * (x * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.7d+181)) .or. (.not. (y <= 1.55d-68))) then
        tmp = (y * t) * -x
    else
        tmp = x - (a * (x * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.7e+181) || !(y <= 1.55e-68)) {
		tmp = (y * t) * -x;
	} else {
		tmp = x - (a * (x * z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.7e+181) or not (y <= 1.55e-68):
		tmp = (y * t) * -x
	else:
		tmp = x - (a * (x * z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.7e+181) || !(y <= 1.55e-68))
		tmp = Float64(Float64(y * t) * Float64(-x));
	else
		tmp = Float64(x - Float64(a * Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.7e+181) || ~((y <= 1.55e-68)))
		tmp = (y * t) * -x;
	else
		tmp = x - (a * (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.7e+181], N[Not[LessEqual[y, 1.55e-68]], $MachinePrecision]], N[(N[(y * t), $MachinePrecision] * (-x)), $MachinePrecision], N[(x - N[(a * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.70000000000000007e181 or 1.55e-68 < y

   1. Initial program 99.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 66.1%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 66.1%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 66.1%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 66.1%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 66.1%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 22.0%

      \[\leadsto \color{blue}{x + -1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 22.0%

         \[\leadsto x + \color{blue}{\left(-t \cdot \left(x \cdot y\right)\right)} \]

      2. unsub-neg 22.0%

         \[\leadsto \color{blue}{x - t \cdot \left(x \cdot y\right)} \]

      3. *-commutative 22.0%

         \[\leadsto x - \color{blue}{\left(x \cdot y\right) \cdot t} \]

      4. *-commutative 22.0%

         \[\leadsto x - \color{blue}{\left(y \cdot x\right)} \cdot t \]

      5. associate-*l* 20.2%

         \[\leadsto x - \color{blue}{y \cdot \left(x \cdot t\right)} \]

      6. *-commutative 20.2%

         \[\leadsto x - y \cdot \color{blue}{\left(t \cdot x\right)} \]

   8. Simplified 20.2%

      \[\leadsto \color{blue}{x - y \cdot \left(t \cdot x\right)} \]

   9. Taylor expanded in y around inf 23.3%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 23.3%

          \[\leadsto \color{blue}{-t \cdot \left(x \cdot y\right)} \]

       2. *-commutative 23.3%

          \[\leadsto -\color{blue}{\left(x \cdot y\right) \cdot t} \]

       3. associate-*r* 27.2%

          \[\leadsto -\color{blue}{x \cdot \left(y \cdot t\right)} \]

       4. *-commutative 27.2%

          \[\leadsto -\color{blue}{\left(y \cdot t\right) \cdot x} \]

       5. distribute-rgt-neg-in 27.2%

          \[\leadsto \color{blue}{\left(y \cdot t\right) \cdot \left(-x\right)} \]

   11. Simplified 27.2%

       \[\leadsto \color{blue}{\left(y \cdot t\right) \cdot \left(-x\right)} \]

   if -2.70000000000000007e181 < y < 1.55e-68

   1. Initial program 94.4%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 70.2%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\log \left(1 - z\right) - b\right)}} \]
   4. Step-by-step derivation

      1. sub-neg 70.2%

         \[\leadsto x \cdot e^{a \cdot \left(\log \color{blue}{\left(1 + \left(-z\right)\right)} - b\right)} \]

      2. log1p-define 77.0%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 77.0%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in b around 0 31.4%

      \[\leadsto \color{blue}{x \cdot {\left(1 - z\right)}^{a}} \]

   7. Taylor expanded in z around 0 32.4%

      \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(x \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 32.4%

         \[\leadsto x + \color{blue}{\left(-a \cdot \left(x \cdot z\right)\right)} \]

      2. unsub-neg 32.4%

         \[\leadsto \color{blue}{x - a \cdot \left(x \cdot z\right)} \]

      3. *-commutative 32.4%

         \[\leadsto x - a \cdot \color{blue}{\left(z \cdot x\right)} \]

   9. Simplified 32.4%

      \[\leadsto \color{blue}{x - a \cdot \left(z \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 30.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+181} \lor \neg \left(y \leq 1.55 \cdot 10^{-68}\right):\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 26.6% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+181} \lor \neg \left(y \leq 1.55 \cdot 10^{-68}\right):\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.7e+181) (not (<= y 1.55e-68)))
   (* (* y t) (- x))
   (* x (- 1.0 (* z a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.7e+181) || !(y <= 1.55e-68)) {
		tmp = (y * t) * -x;
	} else {
		tmp = x * (1.0 - (z * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.7d+181)) .or. (.not. (y <= 1.55d-68))) then
        tmp = (y * t) * -x
    else
        tmp = x * (1.0d0 - (z * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.7e+181) || !(y <= 1.55e-68)) {
		tmp = (y * t) * -x;
	} else {
		tmp = x * (1.0 - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.7e+181) or not (y <= 1.55e-68):
		tmp = (y * t) * -x
	else:
		tmp = x * (1.0 - (z * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.7e+181) || !(y <= 1.55e-68))
		tmp = Float64(Float64(y * t) * Float64(-x));
	else
		tmp = Float64(x * Float64(1.0 - Float64(z * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.7e+181) || ~((y <= 1.55e-68)))
		tmp = (y * t) * -x;
	else
		tmp = x * (1.0 - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.7e+181], N[Not[LessEqual[y, 1.55e-68]], $MachinePrecision]], N[(N[(y * t), $MachinePrecision] * (-x)), $MachinePrecision], N[(x * N[(1.0 - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.70000000000000007e181 or 1.55e-68 < y

   1. Initial program 99.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 66.1%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 66.1%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 66.1%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 66.1%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 66.1%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 22.0%

      \[\leadsto \color{blue}{x + -1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 22.0%

         \[\leadsto x + \color{blue}{\left(-t \cdot \left(x \cdot y\right)\right)} \]

      2. unsub-neg 22.0%

         \[\leadsto \color{blue}{x - t \cdot \left(x \cdot y\right)} \]

      3. *-commutative 22.0%

         \[\leadsto x - \color{blue}{\left(x \cdot y\right) \cdot t} \]

      4. *-commutative 22.0%

         \[\leadsto x - \color{blue}{\left(y \cdot x\right)} \cdot t \]

      5. associate-*l* 20.2%

         \[\leadsto x - \color{blue}{y \cdot \left(x \cdot t\right)} \]

      6. *-commutative 20.2%

         \[\leadsto x - y \cdot \color{blue}{\left(t \cdot x\right)} \]

   8. Simplified 20.2%

      \[\leadsto \color{blue}{x - y \cdot \left(t \cdot x\right)} \]

   9. Taylor expanded in y around inf 23.3%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 23.3%

          \[\leadsto \color{blue}{-t \cdot \left(x \cdot y\right)} \]

       2. *-commutative 23.3%

          \[\leadsto -\color{blue}{\left(x \cdot y\right) \cdot t} \]

       3. associate-*r* 27.2%

          \[\leadsto -\color{blue}{x \cdot \left(y \cdot t\right)} \]

       4. *-commutative 27.2%

          \[\leadsto -\color{blue}{\left(y \cdot t\right) \cdot x} \]

       5. distribute-rgt-neg-in 27.2%

          \[\leadsto \color{blue}{\left(y \cdot t\right) \cdot \left(-x\right)} \]

   11. Simplified 27.2%

       \[\leadsto \color{blue}{\left(y \cdot t\right) \cdot \left(-x\right)} \]

   if -2.70000000000000007e181 < y < 1.55e-68

   1. Initial program 94.4%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 70.2%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\log \left(1 - z\right) - b\right)}} \]
   4. Step-by-step derivation

      1. sub-neg 70.2%

         \[\leadsto x \cdot e^{a \cdot \left(\log \color{blue}{\left(1 + \left(-z\right)\right)} - b\right)} \]

      2. log1p-define 77.0%

         \[\leadsto x \cdot e^{a \cdot \left(\color{blue}{\mathsf{log1p}\left(-z\right)} - b\right)} \]

   5. Simplified 77.0%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(\mathsf{log1p}\left(-z\right) - b\right)}} \]

   6. Taylor expanded in b around 0 31.4%

      \[\leadsto \color{blue}{x \cdot {\left(1 - z\right)}^{a}} \]

   7. Taylor expanded in z around 0 32.3%

      \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \left(a \cdot z\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 32.3%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(-a \cdot z\right)}\right) \]

      2. unsub-neg 32.3%

         \[\leadsto x \cdot \color{blue}{\left(1 - a \cdot z\right)} \]

   9. Simplified 32.3%

      \[\leadsto x \cdot \color{blue}{\left(1 - a \cdot z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 30.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+181} \lor \neg \left(y \leq 1.55 \cdot 10^{-68}\right):\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 30.4% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+200}:\\ \;\;\;\;x - t \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-68}:\\ \;\;\;\;x - b \cdot \left(x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.3e+200)
   (- x (* t (* x y)))
   (if (<= y 1.55e-68) (- x (* b (* x a))) (* (* y t) (- x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.3e+200) {
		tmp = x - (t * (x * y));
	} else if (y <= 1.55e-68) {
		tmp = x - (b * (x * a));
	} else {
		tmp = (y * t) * -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-2.3d+200)) then
        tmp = x - (t * (x * y))
    else if (y <= 1.55d-68) then
        tmp = x - (b * (x * a))
    else
        tmp = (y * t) * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.3e+200) {
		tmp = x - (t * (x * y));
	} else if (y <= 1.55e-68) {
		tmp = x - (b * (x * a));
	} else {
		tmp = (y * t) * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.3e+200:
		tmp = x - (t * (x * y))
	elif y <= 1.55e-68:
		tmp = x - (b * (x * a))
	else:
		tmp = (y * t) * -x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.3e+200)
		tmp = Float64(x - Float64(t * Float64(x * y)));
	elseif (y <= 1.55e-68)
		tmp = Float64(x - Float64(b * Float64(x * a)));
	else
		tmp = Float64(Float64(y * t) * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.3e+200)
		tmp = x - (t * (x * y));
	elseif (y <= 1.55e-68)
		tmp = x - (b * (x * a));
	else
		tmp = (y * t) * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.3e+200], N[(x - N[(t * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e-68], N[(x - N[(b * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * t), $MachinePrecision] * (-x)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.30000000000000003e200

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 74.1%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 74.1%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 74.1%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 74.1%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 74.1%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 43.3%

      \[\leadsto \color{blue}{x + -1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 43.3%

         \[\leadsto x + \color{blue}{\left(-t \cdot \left(x \cdot y\right)\right)} \]

      2. unsub-neg 43.3%

         \[\leadsto \color{blue}{x - t \cdot \left(x \cdot y\right)} \]

      3. *-commutative 43.3%

         \[\leadsto x - \color{blue}{\left(x \cdot y\right) \cdot t} \]

      4. *-commutative 43.3%

         \[\leadsto x - \color{blue}{\left(y \cdot x\right)} \cdot t \]

      5. associate-*l* 38.5%

         \[\leadsto x - \color{blue}{y \cdot \left(x \cdot t\right)} \]

      6. *-commutative 38.5%

         \[\leadsto x - y \cdot \color{blue}{\left(t \cdot x\right)} \]

   8. Simplified 38.5%

      \[\leadsto \color{blue}{x - y \cdot \left(t \cdot x\right)} \]

   9. Taylor expanded in y around 0 43.3%

      \[\leadsto x - \color{blue}{t \cdot \left(x \cdot y\right)} \]
   10. Step-by-step derivation

       1. *-commutative 43.3%

          \[\leadsto x - t \cdot \color{blue}{\left(y \cdot x\right)} \]

   11. Simplified 43.3%

       \[\leadsto x - \color{blue}{t \cdot \left(y \cdot x\right)} \]

   if -2.30000000000000003e200 < y < 1.55e-68

   1. Initial program 94.6%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 68.3%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(a \cdot b\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 68.3%

         \[\leadsto x \cdot e^{\color{blue}{-a \cdot b}} \]

      2. distribute-rgt-neg-out 68.3%

         \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

   5. Simplified 68.3%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

   6. Taylor expanded in a around 0 37.4%

      \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 37.4%

         \[\leadsto x + \color{blue}{\left(-a \cdot \left(b \cdot x\right)\right)} \]

      2. unsub-neg 37.4%

         \[\leadsto \color{blue}{x - a \cdot \left(b \cdot x\right)} \]

      3. associate-*r* 39.7%

         \[\leadsto x - \color{blue}{\left(a \cdot b\right) \cdot x} \]

      4. *-commutative 39.7%

         \[\leadsto x - \color{blue}{\left(b \cdot a\right)} \cdot x \]

      5. associate-*l* 38.9%

         \[\leadsto x - \color{blue}{b \cdot \left(a \cdot x\right)} \]

   8. Simplified 38.9%

      \[\leadsto \color{blue}{x - b \cdot \left(a \cdot x\right)} \]

   if 1.55e-68 < y

   1. Initial program 98.6%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 63.9%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 63.9%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 63.9%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 63.9%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 63.9%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 18.2%

      \[\leadsto \color{blue}{x + -1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 18.2%

         \[\leadsto x + \color{blue}{\left(-t \cdot \left(x \cdot y\right)\right)} \]

      2. unsub-neg 18.2%

         \[\leadsto \color{blue}{x - t \cdot \left(x \cdot y\right)} \]

      3. *-commutative 18.2%

         \[\leadsto x - \color{blue}{\left(x \cdot y\right) \cdot t} \]

      4. *-commutative 18.2%

         \[\leadsto x - \color{blue}{\left(y \cdot x\right)} \cdot t \]

      5. associate-*l* 17.0%

         \[\leadsto x - \color{blue}{y \cdot \left(x \cdot t\right)} \]

      6. *-commutative 17.0%

         \[\leadsto x - y \cdot \color{blue}{\left(t \cdot x\right)} \]

   8. Simplified 17.0%

      \[\leadsto \color{blue}{x - y \cdot \left(t \cdot x\right)} \]

   9. Taylor expanded in y around inf 20.0%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 20.0%

          \[\leadsto \color{blue}{-t \cdot \left(x \cdot y\right)} \]

       2. *-commutative 20.0%

          \[\leadsto -\color{blue}{\left(x \cdot y\right) \cdot t} \]

       3. associate-*r* 25.1%

          \[\leadsto -\color{blue}{x \cdot \left(y \cdot t\right)} \]

       4. *-commutative 25.1%

          \[\leadsto -\color{blue}{\left(y \cdot t\right) \cdot x} \]

       5. distribute-rgt-neg-in 25.1%

          \[\leadsto \color{blue}{\left(y \cdot t\right) \cdot \left(-x\right)} \]

   11. Simplified 25.1%

       \[\leadsto \color{blue}{\left(y \cdot t\right) \cdot \left(-x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 35.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+200}:\\ \;\;\;\;x - t \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-68}:\\ \;\;\;\;x - b \cdot \left(x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 30.4% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+198}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-68}:\\ \;\;\;\;x - b \cdot \left(x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -9e+198)
   (* t (* y (- x)))
   (if (<= y 1.55e-68) (- x (* b (* x a))) (* (* y t) (- x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -9e+198) {
		tmp = t * (y * -x);
	} else if (y <= 1.55e-68) {
		tmp = x - (b * (x * a));
	} else {
		tmp = (y * t) * -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-9d+198)) then
        tmp = t * (y * -x)
    else if (y <= 1.55d-68) then
        tmp = x - (b * (x * a))
    else
        tmp = (y * t) * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -9e+198) {
		tmp = t * (y * -x);
	} else if (y <= 1.55e-68) {
		tmp = x - (b * (x * a));
	} else {
		tmp = (y * t) * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -9e+198:
		tmp = t * (y * -x)
	elif y <= 1.55e-68:
		tmp = x - (b * (x * a))
	else:
		tmp = (y * t) * -x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -9e+198)
		tmp = Float64(t * Float64(y * Float64(-x)));
	elseif (y <= 1.55e-68)
		tmp = Float64(x - Float64(b * Float64(x * a)));
	else
		tmp = Float64(Float64(y * t) * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -9e+198)
		tmp = t * (y * -x);
	elseif (y <= 1.55e-68)
		tmp = x - (b * (x * a));
	else
		tmp = (y * t) * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -9e+198], N[(t * N[(y * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e-68], N[(x - N[(b * N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * t), $MachinePrecision] * (-x)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.00000000000000003e198

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 74.1%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 74.1%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 74.1%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 74.1%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 74.1%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 43.3%

      \[\leadsto \color{blue}{x + -1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 43.3%

         \[\leadsto x + \color{blue}{\left(-t \cdot \left(x \cdot y\right)\right)} \]

      2. unsub-neg 43.3%

         \[\leadsto \color{blue}{x - t \cdot \left(x \cdot y\right)} \]

      3. *-commutative 43.3%

         \[\leadsto x - \color{blue}{\left(x \cdot y\right) \cdot t} \]

      4. *-commutative 43.3%

         \[\leadsto x - \color{blue}{\left(y \cdot x\right)} \cdot t \]

      5. associate-*l* 38.5%

         \[\leadsto x - \color{blue}{y \cdot \left(x \cdot t\right)} \]

      6. *-commutative 38.5%

         \[\leadsto x - y \cdot \color{blue}{\left(t \cdot x\right)} \]

   8. Simplified 38.5%

      \[\leadsto \color{blue}{x - y \cdot \left(t \cdot x\right)} \]

   9. Taylor expanded in y around inf 43.2%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 43.2%

          \[\leadsto \color{blue}{-t \cdot \left(x \cdot y\right)} \]

       2. *-commutative 43.2%

          \[\leadsto -\color{blue}{\left(x \cdot y\right) \cdot t} \]

       3. associate-*r* 38.3%

          \[\leadsto -\color{blue}{x \cdot \left(y \cdot t\right)} \]

       4. *-commutative 38.3%

          \[\leadsto -\color{blue}{\left(y \cdot t\right) \cdot x} \]

       5. distribute-rgt-neg-in 38.3%

          \[\leadsto \color{blue}{\left(y \cdot t\right) \cdot \left(-x\right)} \]

   11. Simplified 38.3%

       \[\leadsto \color{blue}{\left(y \cdot t\right) \cdot \left(-x\right)} \]

   12. Taylor expanded in y around 0 43.2%

       \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   13. Step-by-step derivation

       1. associate-*r* 43.2%

          \[\leadsto \color{blue}{\left(-1 \cdot t\right) \cdot \left(x \cdot y\right)} \]

       2. neg-mul-1 43.2%

          \[\leadsto \color{blue}{\left(-t\right)} \cdot \left(x \cdot y\right) \]

       3. *-commutative 43.2%

          \[\leadsto \left(-t\right) \cdot \color{blue}{\left(y \cdot x\right)} \]

   14. Simplified 43.2%

       \[\leadsto \color{blue}{\left(-t\right) \cdot \left(y \cdot x\right)} \]

   if -9.00000000000000003e198 < y < 1.55e-68

   1. Initial program 94.6%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 68.3%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(a \cdot b\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 68.3%

         \[\leadsto x \cdot e^{\color{blue}{-a \cdot b}} \]

      2. distribute-rgt-neg-out 68.3%

         \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

   5. Simplified 68.3%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

   6. Taylor expanded in a around 0 37.4%

      \[\leadsto \color{blue}{x + -1 \cdot \left(a \cdot \left(b \cdot x\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 37.4%

         \[\leadsto x + \color{blue}{\left(-a \cdot \left(b \cdot x\right)\right)} \]

      2. unsub-neg 37.4%

         \[\leadsto \color{blue}{x - a \cdot \left(b \cdot x\right)} \]

      3. associate-*r* 39.7%

         \[\leadsto x - \color{blue}{\left(a \cdot b\right) \cdot x} \]

      4. *-commutative 39.7%

         \[\leadsto x - \color{blue}{\left(b \cdot a\right)} \cdot x \]

      5. associate-*l* 38.9%

         \[\leadsto x - \color{blue}{b \cdot \left(a \cdot x\right)} \]

   8. Simplified 38.9%

      \[\leadsto \color{blue}{x - b \cdot \left(a \cdot x\right)} \]

   if 1.55e-68 < y

   1. Initial program 98.6%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 63.9%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 63.9%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 63.9%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 63.9%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 63.9%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 18.2%

      \[\leadsto \color{blue}{x + -1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 18.2%

         \[\leadsto x + \color{blue}{\left(-t \cdot \left(x \cdot y\right)\right)} \]

      2. unsub-neg 18.2%

         \[\leadsto \color{blue}{x - t \cdot \left(x \cdot y\right)} \]

      3. *-commutative 18.2%

         \[\leadsto x - \color{blue}{\left(x \cdot y\right) \cdot t} \]

      4. *-commutative 18.2%

         \[\leadsto x - \color{blue}{\left(y \cdot x\right)} \cdot t \]

      5. associate-*l* 17.0%

         \[\leadsto x - \color{blue}{y \cdot \left(x \cdot t\right)} \]

      6. *-commutative 17.0%

         \[\leadsto x - y \cdot \color{blue}{\left(t \cdot x\right)} \]

   8. Simplified 17.0%

      \[\leadsto \color{blue}{x - y \cdot \left(t \cdot x\right)} \]

   9. Taylor expanded in y around inf 20.0%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 20.0%

          \[\leadsto \color{blue}{-t \cdot \left(x \cdot y\right)} \]

       2. *-commutative 20.0%

          \[\leadsto -\color{blue}{\left(x \cdot y\right) \cdot t} \]

       3. associate-*r* 25.1%

          \[\leadsto -\color{blue}{x \cdot \left(y \cdot t\right)} \]

       4. *-commutative 25.1%

          \[\leadsto -\color{blue}{\left(y \cdot t\right) \cdot x} \]

       5. distribute-rgt-neg-in 25.1%

          \[\leadsto \color{blue}{\left(y \cdot t\right) \cdot \left(-x\right)} \]

   11. Simplified 25.1%

       \[\leadsto \color{blue}{\left(y \cdot t\right) \cdot \left(-x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 35.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+198}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-68}:\\ \;\;\;\;x - b \cdot \left(x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 25.9% accurate, 19.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.7 \cdot 10^{+198} \lor \neg \left(y \leq 4.5 \cdot 10^{-69}\right):\\ \;\;\;\;y \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -7.7e+198) (not (<= y 4.5e-69))) (* y (* t (- x))) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -7.7e+198) || !(y <= 4.5e-69)) {
		tmp = y * (t * -x);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-7.7d+198)) .or. (.not. (y <= 4.5d-69))) then
        tmp = y * (t * -x)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -7.7e+198) || !(y <= 4.5e-69)) {
		tmp = y * (t * -x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -7.7e+198) or not (y <= 4.5e-69):
		tmp = y * (t * -x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -7.7e+198) || !(y <= 4.5e-69))
		tmp = Float64(y * Float64(t * Float64(-x)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -7.7e+198) || ~((y <= 4.5e-69)))
		tmp = y * (t * -x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -7.7e+198], N[Not[LessEqual[y, 4.5e-69]], $MachinePrecision]], N[(y * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -7.70000000000000039e198 or 4.50000000000000009e-69 < y

   1. Initial program 98.9%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 66.0%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 66.0%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 66.0%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 66.0%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 66.0%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 23.3%

      \[\leadsto \color{blue}{x + -1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 23.3%

         \[\leadsto x + \color{blue}{\left(-t \cdot \left(x \cdot y\right)\right)} \]

      2. unsub-neg 23.3%

         \[\leadsto \color{blue}{x - t \cdot \left(x \cdot y\right)} \]

      3. *-commutative 23.3%

         \[\leadsto x - \color{blue}{\left(x \cdot y\right) \cdot t} \]

      4. *-commutative 23.3%

         \[\leadsto x - \color{blue}{\left(y \cdot x\right)} \cdot t \]

      5. associate-*l* 21.4%

         \[\leadsto x - \color{blue}{y \cdot \left(x \cdot t\right)} \]

      6. *-commutative 21.4%

         \[\leadsto x - y \cdot \color{blue}{\left(t \cdot x\right)} \]

   8. Simplified 21.4%

      \[\leadsto \color{blue}{x - y \cdot \left(t \cdot x\right)} \]

   9. Taylor expanded in y around inf 23.4%

      \[\leadsto \color{blue}{y \cdot \left(\frac{x}{y} - t \cdot x\right)} \]

   10. Taylor expanded in y around inf 25.9%

       \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 25.9%

          \[\leadsto y \cdot \color{blue}{\left(\left(-1 \cdot t\right) \cdot x\right)} \]

       2. neg-mul-1 25.9%

          \[\leadsto y \cdot \left(\color{blue}{\left(-t\right)} \cdot x\right) \]

   12. Simplified 25.9%

       \[\leadsto y \cdot \color{blue}{\left(\left(-t\right) \cdot x\right)} \]

   if -7.70000000000000039e198 < y < 4.50000000000000009e-69

   1. Initial program 94.6%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 68.3%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(a \cdot b\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 68.3%

         \[\leadsto x \cdot e^{\color{blue}{-a \cdot b}} \]

      2. distribute-rgt-neg-out 68.3%

         \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

   5. Simplified 68.3%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

   6. Taylor expanded in a around 0 28.5%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 27.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.7 \cdot 10^{+198} \lor \neg \left(y \leq 4.5 \cdot 10^{-69}\right):\\ \;\;\;\;y \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 25.7% accurate, 19.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.7 \cdot 10^{+198}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-68}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -7.7e+198)
   (* t (* y (- x)))
   (if (<= y 1.55e-68) x (* (* y t) (- x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -7.7e+198) {
		tmp = t * (y * -x);
	} else if (y <= 1.55e-68) {
		tmp = x;
	} else {
		tmp = (y * t) * -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-7.7d+198)) then
        tmp = t * (y * -x)
    else if (y <= 1.55d-68) then
        tmp = x
    else
        tmp = (y * t) * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -7.7e+198) {
		tmp = t * (y * -x);
	} else if (y <= 1.55e-68) {
		tmp = x;
	} else {
		tmp = (y * t) * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -7.7e+198:
		tmp = t * (y * -x)
	elif y <= 1.55e-68:
		tmp = x
	else:
		tmp = (y * t) * -x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -7.7e+198)
		tmp = Float64(t * Float64(y * Float64(-x)));
	elseif (y <= 1.55e-68)
		tmp = x;
	else
		tmp = Float64(Float64(y * t) * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -7.7e+198)
		tmp = t * (y * -x);
	elseif (y <= 1.55e-68)
		tmp = x;
	else
		tmp = (y * t) * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -7.7e+198], N[(t * N[(y * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e-68], x, N[(N[(y * t), $MachinePrecision] * (-x)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.70000000000000039e198

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 74.1%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 74.1%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 74.1%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 74.1%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 74.1%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 43.3%

      \[\leadsto \color{blue}{x + -1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 43.3%

         \[\leadsto x + \color{blue}{\left(-t \cdot \left(x \cdot y\right)\right)} \]

      2. unsub-neg 43.3%

         \[\leadsto \color{blue}{x - t \cdot \left(x \cdot y\right)} \]

      3. *-commutative 43.3%

         \[\leadsto x - \color{blue}{\left(x \cdot y\right) \cdot t} \]

      4. *-commutative 43.3%

         \[\leadsto x - \color{blue}{\left(y \cdot x\right)} \cdot t \]

      5. associate-*l* 38.5%

         \[\leadsto x - \color{blue}{y \cdot \left(x \cdot t\right)} \]

      6. *-commutative 38.5%

         \[\leadsto x - y \cdot \color{blue}{\left(t \cdot x\right)} \]

   8. Simplified 38.5%

      \[\leadsto \color{blue}{x - y \cdot \left(t \cdot x\right)} \]

   9. Taylor expanded in y around inf 43.2%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 43.2%

          \[\leadsto \color{blue}{-t \cdot \left(x \cdot y\right)} \]

       2. *-commutative 43.2%

          \[\leadsto -\color{blue}{\left(x \cdot y\right) \cdot t} \]

       3. associate-*r* 38.3%

          \[\leadsto -\color{blue}{x \cdot \left(y \cdot t\right)} \]

       4. *-commutative 38.3%

          \[\leadsto -\color{blue}{\left(y \cdot t\right) \cdot x} \]

       5. distribute-rgt-neg-in 38.3%

          \[\leadsto \color{blue}{\left(y \cdot t\right) \cdot \left(-x\right)} \]

   11. Simplified 38.3%

       \[\leadsto \color{blue}{\left(y \cdot t\right) \cdot \left(-x\right)} \]

   12. Taylor expanded in y around 0 43.2%

       \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   13. Step-by-step derivation

       1. associate-*r* 43.2%

          \[\leadsto \color{blue}{\left(-1 \cdot t\right) \cdot \left(x \cdot y\right)} \]

       2. neg-mul-1 43.2%

          \[\leadsto \color{blue}{\left(-t\right)} \cdot \left(x \cdot y\right) \]

       3. *-commutative 43.2%

          \[\leadsto \left(-t\right) \cdot \color{blue}{\left(y \cdot x\right)} \]

   14. Simplified 43.2%

       \[\leadsto \color{blue}{\left(-t\right) \cdot \left(y \cdot x\right)} \]

   if -7.70000000000000039e198 < y < 1.55e-68

   1. Initial program 94.6%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 68.3%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(a \cdot b\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 68.3%

         \[\leadsto x \cdot e^{\color{blue}{-a \cdot b}} \]

      2. distribute-rgt-neg-out 68.3%

         \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

   5. Simplified 68.3%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

   6. Taylor expanded in a around 0 28.5%

      \[\leadsto \color{blue}{x} \]

   if 1.55e-68 < y

   1. Initial program 98.6%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 63.9%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 63.9%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 63.9%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 63.9%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 63.9%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 18.2%

      \[\leadsto \color{blue}{x + -1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 18.2%

         \[\leadsto x + \color{blue}{\left(-t \cdot \left(x \cdot y\right)\right)} \]

      2. unsub-neg 18.2%

         \[\leadsto \color{blue}{x - t \cdot \left(x \cdot y\right)} \]

      3. *-commutative 18.2%

         \[\leadsto x - \color{blue}{\left(x \cdot y\right) \cdot t} \]

      4. *-commutative 18.2%

         \[\leadsto x - \color{blue}{\left(y \cdot x\right)} \cdot t \]

      5. associate-*l* 17.0%

         \[\leadsto x - \color{blue}{y \cdot \left(x \cdot t\right)} \]

      6. *-commutative 17.0%

         \[\leadsto x - y \cdot \color{blue}{\left(t \cdot x\right)} \]

   8. Simplified 17.0%

      \[\leadsto \color{blue}{x - y \cdot \left(t \cdot x\right)} \]

   9. Taylor expanded in y around inf 20.0%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 20.0%

          \[\leadsto \color{blue}{-t \cdot \left(x \cdot y\right)} \]

       2. *-commutative 20.0%

          \[\leadsto -\color{blue}{\left(x \cdot y\right) \cdot t} \]

       3. associate-*r* 25.1%

          \[\leadsto -\color{blue}{x \cdot \left(y \cdot t\right)} \]

       4. *-commutative 25.1%

          \[\leadsto -\color{blue}{\left(y \cdot t\right) \cdot x} \]

       5. distribute-rgt-neg-in 25.1%

          \[\leadsto \color{blue}{\left(y \cdot t\right) \cdot \left(-x\right)} \]

   11. Simplified 25.1%

       \[\leadsto \color{blue}{\left(y \cdot t\right) \cdot \left(-x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 28.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.7 \cdot 10^{+198}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-68}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 26.2% accurate, 19.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.7 \cdot 10^{+198}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-68}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -7.7e+198)
   (* t (* y (- x)))
   (if (<= y 1.55e-68) x (* y (* t (- x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -7.7e+198) {
		tmp = t * (y * -x);
	} else if (y <= 1.55e-68) {
		tmp = x;
	} else {
		tmp = y * (t * -x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-7.7d+198)) then
        tmp = t * (y * -x)
    else if (y <= 1.55d-68) then
        tmp = x
    else
        tmp = y * (t * -x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -7.7e+198) {
		tmp = t * (y * -x);
	} else if (y <= 1.55e-68) {
		tmp = x;
	} else {
		tmp = y * (t * -x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -7.7e+198:
		tmp = t * (y * -x)
	elif y <= 1.55e-68:
		tmp = x
	else:
		tmp = y * (t * -x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -7.7e+198)
		tmp = Float64(t * Float64(y * Float64(-x)));
	elseif (y <= 1.55e-68)
		tmp = x;
	else
		tmp = Float64(y * Float64(t * Float64(-x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -7.7e+198)
		tmp = t * (y * -x);
	elseif (y <= 1.55e-68)
		tmp = x;
	else
		tmp = y * (t * -x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -7.7e+198], N[(t * N[(y * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e-68], x, N[(y * N[(t * (-x)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.70000000000000039e198

   1. Initial program 100.0%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 74.1%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 74.1%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 74.1%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 74.1%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 74.1%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 43.3%

      \[\leadsto \color{blue}{x + -1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 43.3%

         \[\leadsto x + \color{blue}{\left(-t \cdot \left(x \cdot y\right)\right)} \]

      2. unsub-neg 43.3%

         \[\leadsto \color{blue}{x - t \cdot \left(x \cdot y\right)} \]

      3. *-commutative 43.3%

         \[\leadsto x - \color{blue}{\left(x \cdot y\right) \cdot t} \]

      4. *-commutative 43.3%

         \[\leadsto x - \color{blue}{\left(y \cdot x\right)} \cdot t \]

      5. associate-*l* 38.5%

         \[\leadsto x - \color{blue}{y \cdot \left(x \cdot t\right)} \]

      6. *-commutative 38.5%

         \[\leadsto x - y \cdot \color{blue}{\left(t \cdot x\right)} \]

   8. Simplified 38.5%

      \[\leadsto \color{blue}{x - y \cdot \left(t \cdot x\right)} \]

   9. Taylor expanded in y around inf 43.2%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 43.2%

          \[\leadsto \color{blue}{-t \cdot \left(x \cdot y\right)} \]

       2. *-commutative 43.2%

          \[\leadsto -\color{blue}{\left(x \cdot y\right) \cdot t} \]

       3. associate-*r* 38.3%

          \[\leadsto -\color{blue}{x \cdot \left(y \cdot t\right)} \]

       4. *-commutative 38.3%

          \[\leadsto -\color{blue}{\left(y \cdot t\right) \cdot x} \]

       5. distribute-rgt-neg-in 38.3%

          \[\leadsto \color{blue}{\left(y \cdot t\right) \cdot \left(-x\right)} \]

   11. Simplified 38.3%

       \[\leadsto \color{blue}{\left(y \cdot t\right) \cdot \left(-x\right)} \]

   12. Taylor expanded in y around 0 43.2%

       \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   13. Step-by-step derivation

       1. associate-*r* 43.2%

          \[\leadsto \color{blue}{\left(-1 \cdot t\right) \cdot \left(x \cdot y\right)} \]

       2. neg-mul-1 43.2%

          \[\leadsto \color{blue}{\left(-t\right)} \cdot \left(x \cdot y\right) \]

       3. *-commutative 43.2%

          \[\leadsto \left(-t\right) \cdot \color{blue}{\left(y \cdot x\right)} \]

   14. Simplified 43.2%

       \[\leadsto \color{blue}{\left(-t\right) \cdot \left(y \cdot x\right)} \]

   if -7.70000000000000039e198 < y < 1.55e-68

   1. Initial program 94.6%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 68.3%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(a \cdot b\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 68.3%

         \[\leadsto x \cdot e^{\color{blue}{-a \cdot b}} \]

      2. distribute-rgt-neg-out 68.3%

         \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

   5. Simplified 68.3%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

   6. Taylor expanded in a around 0 28.5%

      \[\leadsto \color{blue}{x} \]

   if 1.55e-68 < y

   1. Initial program 98.6%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 63.9%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 63.9%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 63.9%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 63.9%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 63.9%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 18.2%

      \[\leadsto \color{blue}{x + -1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 18.2%

         \[\leadsto x + \color{blue}{\left(-t \cdot \left(x \cdot y\right)\right)} \]

      2. unsub-neg 18.2%

         \[\leadsto \color{blue}{x - t \cdot \left(x \cdot y\right)} \]

      3. *-commutative 18.2%

         \[\leadsto x - \color{blue}{\left(x \cdot y\right) \cdot t} \]

      4. *-commutative 18.2%

         \[\leadsto x - \color{blue}{\left(y \cdot x\right)} \cdot t \]

      5. associate-*l* 17.0%

         \[\leadsto x - \color{blue}{y \cdot \left(x \cdot t\right)} \]

      6. *-commutative 17.0%

         \[\leadsto x - y \cdot \color{blue}{\left(t \cdot x\right)} \]

   8. Simplified 17.0%

      \[\leadsto \color{blue}{x - y \cdot \left(t \cdot x\right)} \]

   9. Taylor expanded in y around inf 19.5%

      \[\leadsto \color{blue}{y \cdot \left(\frac{x}{y} - t \cdot x\right)} \]

   10. Taylor expanded in y around inf 22.7%

       \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 22.7%

          \[\leadsto y \cdot \color{blue}{\left(\left(-1 \cdot t\right) \cdot x\right)} \]

       2. neg-mul-1 22.7%

          \[\leadsto y \cdot \left(\color{blue}{\left(-t\right)} \cdot x\right) \]

   12. Simplified 22.7%

       \[\leadsto y \cdot \color{blue}{\left(\left(-t\right) \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 27.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.7 \cdot 10^{+198}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-68}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t \cdot \left(-x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 23.7% accurate, 31.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4.95 \cdot 10^{+176}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x 4.95e+176) (* y (/ x y)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 4.95e+176) {
		tmp = y * (x / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= 4.95d+176) then
        tmp = y * (x / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 4.95e+176) {
		tmp = y * (x / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 4.95e+176:
		tmp = y * (x / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 4.95e+176)
		tmp = Float64(y * Float64(x / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= 4.95e+176)
		tmp = y * (x / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 4.95e+176], N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if x < 4.95000000000000009e176

   1. Initial program 96.1%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 57.1%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(t \cdot y\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 57.1%

         \[\leadsto x \cdot e^{\color{blue}{-t \cdot y}} \]

      2. distribute-lft-neg-out 57.1%

         \[\leadsto x \cdot e^{\color{blue}{\left(-t\right) \cdot y}} \]

      3. *-commutative 57.1%

         \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   5. Simplified 57.1%

      \[\leadsto x \cdot e^{\color{blue}{y \cdot \left(-t\right)}} \]

   6. Taylor expanded in y around 0 25.5%

      \[\leadsto \color{blue}{x + -1 \cdot \left(t \cdot \left(x \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 25.5%

         \[\leadsto x + \color{blue}{\left(-t \cdot \left(x \cdot y\right)\right)} \]

      2. unsub-neg 25.5%

         \[\leadsto \color{blue}{x - t \cdot \left(x \cdot y\right)} \]

      3. *-commutative 25.5%

         \[\leadsto x - \color{blue}{\left(x \cdot y\right) \cdot t} \]

      4. *-commutative 25.5%

         \[\leadsto x - \color{blue}{\left(y \cdot x\right)} \cdot t \]

      5. associate-*l* 25.1%

         \[\leadsto x - \color{blue}{y \cdot \left(x \cdot t\right)} \]

      6. *-commutative 25.1%

         \[\leadsto x - y \cdot \color{blue}{\left(t \cdot x\right)} \]

   8. Simplified 25.1%

      \[\leadsto \color{blue}{x - y \cdot \left(t \cdot x\right)} \]

   9. Taylor expanded in y around inf 23.4%

      \[\leadsto \color{blue}{y \cdot \left(\frac{x}{y} - t \cdot x\right)} \]

   10. Taylor expanded in y around 0 18.9%

       \[\leadsto y \cdot \color{blue}{\frac{x}{y}} \]

   if 4.95000000000000009e176 < x

   1. Initial program 96.8%

      \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 55.5%

      \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(a \cdot b\right)}} \]
   4. Step-by-step derivation

      1. mul-1-neg 55.5%

         \[\leadsto x \cdot e^{\color{blue}{-a \cdot b}} \]

      2. distribute-rgt-neg-out 55.5%

         \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

   5. Simplified 55.5%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

   6. Taylor expanded in a around 0 22.4%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 17: 19.7% accurate, 315.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

Python

def code(x, y, z, t, a, b):
	return x

Julia

function code(x, y, z, t, a, b)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

1. Initial program 96.1%

   \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)} \]
2. Add Preprocessing

3. Taylor expanded in b around inf 53.6%

   \[\leadsto x \cdot e^{\color{blue}{-1 \cdot \left(a \cdot b\right)}} \]
4. Step-by-step derivation

   1. mul-1-neg 53.6%

      \[\leadsto x \cdot e^{\color{blue}{-a \cdot b}} \]

   2. distribute-rgt-neg-out 53.6%

      \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

5. Simplified 53.6%

   \[\leadsto x \cdot e^{\color{blue}{a \cdot \left(-b\right)}} \]

6. Taylor expanded in a around 0 19.7%

   \[\leadsto \color{blue}{x} \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024108 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaApprox from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))))